Elastic pipe control and compensation with managed pressure drilling

A method of regulating downhole pressure using managed pressure drilling may include calculating an elasticity of a drill string during a drilling operation using a torque and drag model included in a managed pressure drilling (MPD) control system and calculating a surge pressure and a swab pressure acting on the drill string during the drilling operation using a hydraulics model included in the MPD control system. The surge and swab pressures may be based on movement of the drill string and in accordance with the elasticity of the drill string. The method may further include determining a set point pressure using a real-time hydraulics model and the torque and drag model, and operating a MPD choke system based on the set point pressure to regulate a predetermined downhole pressure at a predetermined location in a wellbore.